I just took a look at the deals on onsen hotels in mytrip.net on the 19th.
There seem to be some places in the right price range in several prefectures in that whole West-Central-Japan area - Gifu certainly - also Mie prefecture - Hyogo prefecture. One problem with the nicer onsen is that they are often some way off the beaten track. So I guess the choice depends on which direction you will be coming from on the 19th.